Accurate remaining useful life (RUL) prediction of harmonic drives is essential for ensuring the safety of space manipulators. However, existing data-driven methods tend to use discrete time steps to predict RUL. These approaches ignore the actual physical degradation law of continuous degradation for mechanical equipment. To address this issue, taking neural ordinary differential equations as the core framework, this article proposes a state-adaptive liquid neural network (SALNN), which utilizes its unique liquid time-constant mechanism to characterize the RUL trajectory continuously. Specifically, prior to the prediction stage, a novel health indicator (HI) based on a spectral correlation architecture is constructed, targeting the fault characteristics of harmonic drives. Subsequently, SALNN utilizes a state detection module to perceive device degradation severity from the HI, embedding this as state information into the liquid time-constant, which can endow the network with dynamic properties. This mechanism enables the network to apply differentiated update rates corresponding to distinct degradation states, thereby capturing the physical evolutionary dynamics of the RUL more effectively. Experimental results on harmonic drive datasets and XJTU-SY dataset demonstrate that the proposed method effectively suppresses noise and significantly outperforms other state-of-the-art methods in prediction accuracy.
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